Historically, wheeled vehicles and especially in-line, two-wheeled vehicles such as bicycles, motorcycles, scooters, and the like, have been popular forms of transportation, exercise, and sport. More recently, such vehicles are being used in particularly rugged environments including unimproved roads and rough terrain. For example, similar to a conventional snowboard operating over a snow-covered hill, it is desirable to use an in-line two-wheeled vehicle to travel downhill over rough terrain.
In general, a rider balances on an elongated frame of the vehicle while it is either being propelled by gravity, the rider or self-propelled, and steers the vehicle either by tilting the vehicle, as with a skateboard, or rotating a steering mechanism, such as the handle bar of a conventional bicycle, to turn at least one of the wheels on a fixed axis of rotation. In virtually all uses of such vehicles, it is desirable for the vehicle to travel smoothly, steer easily and responsively, and remain stable during both steady-state and dynamic operation.
The rider on a two-wheeled vehicle is a critical element in the dynamic balancing of the system, which must be stable for successful operation of the vehicle. In particular, similar to a person balancing a stick on his finger, the rider of a two-wheeled vehicle is the active element maintaining stability of the system. The rider develops particular skill to use his or her senses (i.e., eyes, ears, sense of balance, etc.) to detect if there is a need for corrective balancing action, and the degree and type of corrective force needed.
Preferably, stable operation includes the steering wheel remaining in its commanded position (i.e., either aligned straight or at a commanded turn angle) when no dynamic input or other disturbances are acting on the steering mechanism. Such stable operation is particularly desirable, but especially difficult to maintain, when the vehicle is operated over rough terrain and/or at slow speeds.
As children first attempting to ride a bicycle learn, maintaining dynamic balance on a two-wheeled bicycle requires experience and skill. Numerous forces act on a two-wheeled vehicle to keep it dynamically balanced during operation. These forces include gravity, inertia, friction, and gyroscopic forces generated by the spinning wheels. A rider typically manipulates the vehicle by leaning and turning the handlebar to maintain dynamic balance and thereby maneuver the vehicle.
Particularly skilled riders can maintain stable, dynamic balance of traditional bicycles traveling straight without holding the handlebars. In such case, they may even be able to turn their bicycles left or right simply by leaning their body and tilting the vehicle. In general, the faster the bicycle is traveling the easier it is for the rider to maintain such hands-free, stable, dynamic balance. However, minor transient disturbances, such as those associated with riding on an uneven or rough road surface, or the rider needing to change speed or steering directions, quickly destabilize the vehicle.
In more technical terms, for any given two-wheeled vehicle, there is an overall operating envelope of speeds and turn radii for a given terrain in which the vehicle is expected to operate effectively. Similarly, for any given two-wheeled vehicle there is a controllable operating envelope of speeds and turn radii for a given terrain in which the riders' ability to simply tilt the vehicle in one direction or the other is sufficient to correct dynamic instabilities arising during operation of the vehicle, while still maintaining controllability of the vehicle (e.g. also maintaining tilting commanding the vehicle to turn). Unfortunately, with conventional two-wheeled vehicles, the controllable operating envelope is much smaller than the desired operating envelope of the vehicle. Accordingly, traditional two-wheeled vehicles are hand-steered to maintain controllability and stability of the vehicle throughout the entire operating envelope of the vehicle.
Previously, the key elements leading to two-wheeled vehicle stability have not been fully understood. This has limited the size of the controllable operating envelope of traditional two-wheeled vehicles. A typical bicycle or scooter will have a pair of in-line wheels operably secured to a base. Both wheels are typically rotatably secured to the base, such that they rotate freely about their axles to carry the vehicle on a substantially planar running surface. In addition, the front wheel is usually pivotally secured to the base along an axis, commonly known as a steering axis, which is substantially orthogonal to the surface such that the front wheel turns from side-to-side with respect to the base along this axis.
In general, and as discussed more fully in U.S. Pat. No. 5,160,155 to Barachet, the front wheel's point of contact with the planar running surface of the conventional two-wheeled vehicle is behind the point at which a line extended from the steering axis contacts the same surface. The distance between these two points is commonly referred to as the vehicle's “trail.” This orientation allows the front wheel to operate like a conventional caster. Namely, because of a moment arm defined by the trail, the front wheel will turn in the direction of the bases' tilt. Accordingly, to some extent, a rider can steer the vehicle simply by tilting the base to one side.
Conventional two-wheeled vehicle dynamic stability analyses focus on determining the optimal length of the trail for a given design. This process has typically been a trial-and-error approach for a given commercial product. For example, as documented in an article titled “A Fresh Look At Steering Geometry” of the February 1981 issue of Cycling USA, Mathematics professor John Corbet experimented with trail lengths ranging from ⅞ of an inch to 4 5/16 inches. He found that with the trail set at approximately 1⅝ inches the bicycle felt “nervous.” With a trail of 1 3/16 inches, it had “the sort of hands-off stability which seems desirable yet still turns easily,” and with the trail of 2 15/16 inches, “it was very heavy feeling.”
These conventional stability studies of hand-steered two-wheeled vehicles focus on the dynamic stability of the vehicle during straight, steady-state operation. Accordingly, experimentation has found that the larger the trail, the greater the straight, steady-state stability of the vehicle. However, such stability usually comes at the expense of vehicle controllability and dynamic stability of the vehicle during a turn. These studies of hand-steered two-wheeled vehicles are characterized by their qualitative nature and subjective results. Moreover, the studies focus virtually exclusively on the vehicle's trail, and they do not explicitly define the qualities that determine the operational desirability of a vehicle. Instead, they concentrate on “hands-off stability” without defining or evaluating controllability.
Barachet shows two-wheeled vehicles having different caster angles (also referred to as the “rake angle” which is defined as the angle between the steering axis and vertical). Arguably, these figures could be interpreted to suggest that caster angle is another important factor in two-wheeled vehicle stability (i.e. the ability of the vehicle to remain in a state in the presence of disturbances and with no rider input) and control (i.e., the ability of the board to respond in a predictable and desirable manner to rider commanded inputs.) Barachet struggles with finding an optimal design that provides desirable performance over the envelope of operations while having a fixed trail and caster angle. He acknowledges the limitations with his designs by showing several approaches aimed at biasing the steering wheel to a neutral position, and by depending upon unusual athletic techniques of the rider to control and maintain stability of the vehicle.
Another example of the limitations found with conventional analysis of two-wheeled vehicle stability and control can be found in the book Bicycling Science (2nd edition 1995), written by Massachusetts Institute of Technology engineering instructor David Wilson and Frank Whitt. This book summarizes the state-of-the-art of bicycle engineering, and is grounded in solid mathematical-based technical discussions that reflect the support and involvement of a broad spectrum of experts in the field.
A chapter in this book, entitled “Balancing and Steering,” discusses the current state of understanding of in-line, two-wheel vehicle dynamics and the handling qualities of bicycles. It ultimately concludes that “the balancing and steering of bicycles is an extremely complex subject on which there is a great deal of experience and rather little science.”
This situation exists despite the attention of several famous mathematicians and analytical engineers attempting to quantitatively understand these concepts. They conclude that caster angle and trail are important factors in the handling of a two-wheeled vehicle, but they acknowledge that there is no consensus or understanding as to why these elements are important, or if there are other elements that are equally important in understanding the concepts. Accordingly, as with professor John Corbet's work previously described, their work has focused on empirical efforts to quantify the ranges and combinations of these two dimensions as to their relation to “good” handling of a bicycle. This has led to a good understanding of which values and combinations of caster angle and trail that can produce acceptable handling performance, but not much insight as to why.
Some inventors have attempted to improve a wheeled-vehicles' ability to operate over rough terrain. However, such improvements have typically been in the form of introducing improved suspension systems between the wheels and the base of the vehicles. For example, U.S. Pat. No. 5,868,408 to Miller teaches mounting two pair of wheels to a board. One pair of wheels is mounted toward the front of the board and the other pair of wheels is mounted toward the rear of the board. Each pair of wheels is pivotally secured to the board, such that the wheels rotate about respective steering axes. Each wheel is linked to the steering axis through a dynamic linkage that is spring-biased to a neutral position. As one of the wheels hits an obstacle, the spring is compressed, and the wheel is deflected upward to allow the obstacle to pass.
The quality that determines a vehicle's desirability with regards to riding over irregular or rough surfaces is its ability to absorb the influence of the terrain or isolate the rider from the influence of the terrain without diminishing the rider's ability to control the vehicle. As described above, much effort has been expended designing and implementing suspensions that will absorb the dynamics of the terrain by putting suspension systems between the wheels and the base of the vehicle. Although this approach offers some benefits, it does not change the inherent characteristics of the vehicle that determine the susceptibility to the roughness of the terrain or ability to remain controllable particularly at slow speeds.
There are two axes associated with a vehicle that are pertinent to the dynamics that are induced by the terrain. These are the vehicle's roll axis (which runs longitudinally through the vehicle and is nominally horizontal) and the pitch axis (which is perpendicular to the roll axis and is nominally horizontal). A four-wheeled vehicle is influenced by terrain roughness about both axes while an in-line two-wheeled vehicle is influenced only about the pitch axis. Therefore, the in-line two-wheeled vehicle is much more accommodating of irregular or rough riding surfaces by its inherent characteristics. This is evidenced by a motorcycle's ability to negotiate much rougher terrain than a four-wheeled vehicle such as a Sport Utility Vehicle.
While the suspension linkages in Miller offer a smoother ride, they do not teach or suggest a way for allowing a two-wheeled vehicle to remain dynamically stable, but still highly maneuverable, during both straight and turning operations.